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Physics-Informed Neural Network for Daily Canopy Size Forecasting in Strawberry Production Using Fused Weather and Image Embeddings

This study developed a hybrid Physics-Informed Neural Network (PINN) that fuses weather data and image-derived green pixel counts to accurately forecast daily strawberry canopy volume, demonstrating superior performance over baseline models for two commercial cultivars under real-world field conditions.

Original authors: Rohan Bagulwar, Won Suk Lee, Shinsuke Agehara, Hongyoung Jeon, Heping Zhu

Published 2026-09-08

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Rohan Bagulwar, Won Suk Lee, Shinsuke Agehara, Hongyoung Jeon, Heping Zhu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet fields of Florida, where strawberries are grown on a massive scale, the health of a plant is often written in its leaves. For farmers, knowing exactly how much green foliage a plant has at any given moment is crucial; it tells them if the crop is thriving, if it is thirsty, or if it is under attack from disease. Traditionally, getting this information meant walking the rows and measuring by hand, a slow and labor-intensive task that offered only a snapshot of the past. In recent years, technology has offered a faster way: cameras that can count the green pixels in a plant's image to estimate its size. However, a simple count of green pixels is not a crystal ball. It tells a farmer what the plant looks like right now, but it struggles to predict what the plant will look like tomorrow, especially when the weather changes unexpectedly. A sudden cold snap or a heavy rain can alter a plant's appearance in ways that a simple camera cannot anticipate, leading to guesses that are biologically impossible, such as a plant shrinking when the weather is actually warming up.

To bridge the gap between what a camera sees and what biology dictates, researchers at the University of Florida and the United States Department of Agriculture developed a new kind of computer program. This system combines two different ways of thinking about growth. The first part relies on the known laws of plant biology, specifically how plants grow faster as they accumulate heat over time, a concept farmers have used for decades to track development. The second part is a flexible learning tool that watches the weather and the daily images to spot short-term quirks, like a temporary dip in green color caused by a cloudy day. By weaving these two approaches together, the researchers created a system that does not just guess the future but respects the rules of nature while still paying attention to the messy reality of the field.

The team tested this system in a strawberry field in Citra, Florida, during the winter of 2025. They set up an autonomous camera station powered by solar panels, which took pictures of the plants every fifteen minutes for nearly a month. They focused on two popular strawberry varieties, one named 'Florida Brilliance' and another called 'Florida Medallion.' The camera captured the plants from above, and the researchers used software to isolate the green leaves from the soil and plastic mulch, counting the number of green pixels to measure the size of the canopy. Alongside these images, the system pulled real-time weather data, including temperature, humidity, and sunlight, to see how the environment influenced the plants day by day.

The core of their innovation was a hybrid computer model that learned from this data. One part of the model followed a smooth, predictable curve based on the total heat the plants had received, ensuring that the predictions always followed a logical biological path where plants generally grow larger as the season warms. The other part of the model acted as a correction mechanism, learning to adjust that smooth prediction up or down based on the specific weather events of the last week. If a cold front hit, the model learned to expect a slight pause in growth or a change in color, rather than blindly following the smooth curve. Crucially, the system was designed with a safety rule: it was forbidden from predicting that a plant would shrink on a day when the heat accumulation was increasing, a biological impossibility that often trips up simpler computer models.

The results showed that this combined approach worked significantly better than using either method alone. For the 'Florida Brilliance' variety, the system predicted the daily size of the plant's canopy with an average error of about 6,996 pixels, a figure that represented a 4.53% difference from the actual measurements. This was a marked improvement over a model that only followed the smooth biological curve, which missed the mark by over 10,000 pixels, and far better than a simple guess that assumed the plant would stay the same size as it did the day before. The system also performed well on the 'Florida Medallion' variety, though the error rate was slightly higher at 16.4%. The researchers noted that this higher error was likely due to the fact that they had much less data for this specific plant, as a severe storm damaged their equipment early in the study, cutting the observation period short. Even with this limited data, the hybrid model still outperformed the simpler methods, proving that the combination of biological rules and weather-aware learning was robust.

What makes this finding particularly valuable is that the computer model did not just produce a number; it also learned the specific growth characteristics of the strawberries it was watching. Without being told the answers in advance, the system figured out the maximum size the plants could reach and the speed at which they grew, values that matched what the researchers observed in the field. This suggests that the model is not just memorizing the data but is actually understanding the underlying biology. The researchers found that the system could run on a small, inexpensive computer the size of a credit card, making it feasible for farmers to use in real-time without needing expensive servers or constant internet access.

The study highlights a path forward for precision agriculture, where technology helps farmers make decisions before problems become visible to the naked eye. By predicting how a plant will respond to the coming weather, a grower could potentially water or feed their crops at the exact moment they need it, rather than waiting for signs of stress to appear. While the current system was tested over a relatively short period and focused on the early growth stages, the researchers suggest that with more data and better ways to handle changing light conditions, this approach could be expanded to cover the entire growing season. The work demonstrates that when computer science respects the fundamental laws of biology, it can create tools that are not only accurate but also trustworthy for the people who rely on them to feed the world.

Technical Summary: Physics-Informed Neural Network for Daily Canopy Size Forecasting in Strawberry Production

Problem Statement
Strawberry production in Florida requires precise canopy management to optimize water, nutrient application, and stress detection. While green pixel counting from images offers a low-cost proxy for canopy volume, existing technologies lack the ability to forecast future canopy growth or integrate physiological drivers (such as thermal accumulation) with real-time environmental data. Purely data-driven models often fail to generalize across seasons or cultivars, produce biologically implausible predictions (e.g., canopy decline during increasing thermal accumulation), and require large datasets that are often unavailable in experimental farm settings. Conversely, traditional physics-based models (e.g., logistic growth curves driven by Growing Degree Days) capture long-term trends but fail to account for short-term, weather-driven fluctuations.

Methodology
The study proposes a hybrid Physics-Informed Neural Network (PINN) architecture designed to forecast daily strawberry canopy volume (measured in green pixel counts) by fusing weather data and image-derived embeddings.

Data Acquisition: Images were captured every 15 minutes over 38 days for two cultivars ('Florida Brilliance' and 'Florida Medallion') in Citra, FL. Images underwent preprocessing, including manual region extraction, illumination normalization, and HSV thresholding (Hue: 35°–90°, Saturation/Value: 40–255) to isolate green pixels. Weather data (13 variables) were sourced from the Florida Automated Weather Network (FAWN), and Growing Degree Days (GDD) were accumulated using a 7°C base temperature.
Feature Engineering: Daily inputs consisted of a 45-element vector: 13 weather variables and 32 dimensions of image embeddings (derived from a pretrained CNN and reduced via PCA). A 7-day sliding window was used to construct sequences for predicting the 8th day's canopy size.
PINN Architecture: The model comprises two parallel branches:
1. Physics Branch: A learnable three-parameter logistic growth function ( $G(x) = K(1 + e^{-r(x-x_0)})^{-1}$ ) driven by cumulative GDD. This branch captures the deterministic, monotonic biological growth trajectory. Parameters $K$ (asymptote), $r$ (rate), and $x_0$ (inflection point) are learned end-to-end.
2. Data Branch: A single-layer LSTM (hidden size 64) with a Multi-Layer Perceptron (MLP) head processes the 7-day sequence to predict a signed daily residual ( $\Delta$ ). This branch captures stochastic deviations caused by transient weather events (e.g., cold snaps, rain) that the smooth logistic curve cannot explain.
3. Output: The final prediction is the sum of the physics branch output and the LSTM residual ( $\hat{y} = G_{physics} + \Delta$ ).
Training and Regularization: The model was trained using a composite loss function: $L = MSE(\hat{y}, y) + 0.1 \times P$ . The penalty term $P$ activates when GDD increases but the predicted canopy size decreases, enforcing the biological constraint that canopy area should not decline during positive thermal accumulation. The model was trained for 400 epochs using the Adam optimizer.

Key Contributions

Hybrid Architecture for Small Data: The study demonstrates that combining a structured physics prior (logistic growth) with a data-driven residual learner (LSTM) improves forecasting accuracy even with limited training data (approx. 30 days for one cultivar, 7 days for another).
Biological Consistency: By embedding growth constraints directly into the loss function, the model prevents biologically implausible predictions (e.g., canopy shrinkage during heat accumulation), thereby increasing trust in the system for agronomic applications.
Learnable Physical Parameters: Unlike traditional models requiring manual calibration, the PINN learns the logistic parameters ( $K, r, x_0$ ) directly from the data, yielding values consistent with empirical observations (e.g., the learned asymptote $K$ matched the observed maximum canopy size).
Edge Deployment: The system is lightweight (<22,000 parameters) and capable of real-time execution on low-cost hardware (Raspberry Pi 4) with off-grid power capabilities.

Results
The model was evaluated on two cultivars using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE):

'Florida Brilliance' (38-day dataset): The PINN achieved an MAE of 6,996 pixels (MAPE 4.53%) over a five-day test period. This represented a 32% reduction in error compared to a physics-only logistic baseline (MAE 10,260) and a 26% reduction compared to a persistence baseline (MAE 9,416).
'Florida Medallion' (9-day dataset): Despite limited data, the PINN achieved an MAE of 9,440 pixels (MAPE 16.4%) over a two-day test period, outperforming the physics-only baseline (MAE 10,880) and the persistence baseline (MAE 9,580). The model was trained on seven days of data from the nine-day total dataset. The higher error rate for Medallion was attributed to the smaller dataset size and the sensitivity of percentage-based metrics to low absolute pixel counts in smaller plants.
Training Dynamics: The physics penalty term was most active during the first 150 epochs, guiding the model toward biologically consistent behavior before the logistic branch sufficiently adapted to the data, at which point the penalty contribution diminished.

Significance and Claims
The paper claims that this hybrid approach successfully bridges the gap between interpretable agronomic models and flexible machine learning. By anchoring predictions in known biological laws while allowing the neural network to learn short-term environmental deviations, the system provides growers with a "biologically grounded, forward-looking estimate" of canopy development. The authors assert that such a system can be used to detect abnormal growth patterns early, aiding in the management of water, nutrients, and stress mitigation. The study concludes that the architecture is particularly valuable in data-scarce agricultural environments where purely data-driven models risk overfitting or producing untrustworthy outputs. Future work suggested by the authors includes extending the observation period through fruiting phases, replacing raw pixel counts with illumination-invariant indices (like GCC) to reduce lighting artifacts, and exploring multi-plant transfer learning.

Technical Summary: Physics-Informed Neural Network for Daily Canopy Size Forecasting in Strawberry Production

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